I have a VERY small garden, appx 5' X 10', that, after a year where nothing sprouted (not sure why,) I gave up and didn't plant last year. Growing up, my Mom always had a big garden, and I loved all of the fresh veggies. I would love to eventually expand my small garden, but that's another story. Anyway, what's the best way to go from my current problem, which is a garden overgrown with weeds and grass, to a place where I can actually plant. In reading some of the articles, it seems I probably should have prepared the plot in the fall. So, am I too late? Do I need to forget about it again this year, and work on it in the fall?

Never too late to start. Here's a method i typed out a while back you can use to start a new garden. You could do it in a weekend and be planting the next week:

Mow the grass where the garden is to be. Short. Real short! Like down to the soil if you don't mind using your mower that low. Leave it exposed to the sun thru the heat of the day.

If your soil is naturally sour, ie a Ph of less than say 6 1/2, a handful to the square yard of dolomite now will help. If your soil is heavy clay the same amount of gypsum per square yard will also help. (You can buy a Ph test kit for about $10 and they're excellent and will last for many years. Very simple and safe to use).
Then, cover the area with pelletised chook poo. About a handful to the square yard and water it well.

Cover the area in a layer of newspaper at least 10-15 sheets thick. You can use cardboard for this too but the point is don't leave any gaps. Not even the slightest. If you think there's a bit of a gap or a hole in a cardboard box cover it with more paper. The grass WILL come thru otherwise. Refrigerator boxes etc are great for big areas. Have a hose handy to wet the paper or you can bet a breeze will pick up halfway thru this step. Wet the paper at the end of this anyway. Maybe a few stones or half bricks handy just in case.

If the soil is good and you don't need to improve it much go to the last step .

To improve the soil, and i recommend this step even if you have reasonable soil, cover the paper/cardboard with compost, organic soil, pulverised cow/sheep poo, blood and bone, lucerne bales,in fact any organic matter you can get your hands on. More is definitely better. Up to 12" thick is good. 6" will do. If you buy soil, ask what the Ph is and check that it has organic matter incoorporated. Manures and compost are definitely the best though.

Finally, bury the lot under a few bales of spoiled, seed free straw or meadow hay. This should also be a minimum of 6-8" thick. Then water the bed very well.

You can build surrounds for the bed to tidy it up but if you just go around it with a sharp square spade and cut a "V" trench about 4" deep around it you'll stop the grass growing into the garden. Put the soil/grass from this into the compost bin. This trench is easily maintained and aids drainage too. It'll have bits of cardboard or paper hanging out the edges but after about a week you'll be able to go around and just tear them off where they're rotting.
What will happen is the grass underneath will be well fed and warm as toast. It'll want to grow like blazes. But it can't cause it's got no light. So it'll get all soft and just rot and break down. This will cause a nitrogen drop, but the chook poo will supply extra nitrogen and help the process. Also, a squillion critters that you never knew existed will move in and convert the grass and everything else into a rich organic layer of humus. They will carry this into the original soil and do the digging for you. You can use the bed after a few weeks and you'll have a fantastic rich soil with not a chemical added.

As an aside, if it's the right time of the year for planting potatoes, you can put a seed potato every square foot of garden area on top of the layer of cardboard paper and you'll get the best crop of spuds you ever saw. That's a gaurantee. Potatoes are also great for breaking up new soil too so they'll help the digging process
Or you can just spray the grass with glyphosate and spend the next eon trying to improve your soil

A chook is a chicken

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The secret is the soil.